Can some one help i dont get this

Given:

EH is a diameter of the circle.

Measure of arc EF = (10x + 8)°

Measure of arc GH = (11x)°

m∠FDG = 67°

To find:

The value of x, the measure of arc EF and the measure of arc GH in degrees.

Solution:

The measure intercepted angle is equal to the measure of the central angle.

m∠EDF = m(ar EF)

m∠EDF = (10x + 8)°

m∠GDH = m(ar GH)

m∠GDH = (11x)°

Sum of the adjacent angles in a straight line is 180°.

m∠EDF + m∠FDG + m∠GDH = 180°

10x° + 8° + 67° + 11x° = 180°

21x° + 75° = 180°

Subtract 75° from both sides.

21x° = 105°

Divide by 21 on both sides.

x° = 5°

The value of x is 5.

Measure of arc EF = (10(5) + 8)°

                               = 58°

The measure of arc EF is 58°.

Measure of arc GH = (11(5))°

                               = 55°

The measure of arc GH is 55°.

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step-by-step explanation:

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